Study on the regularity of weakly quasi-normal rings
ZHANG Lei
CHEN Huaxi
XU Qingbing
Abstract：A ring R is called weakly quasi-normal(abbreviated as WQN).The class of WQN rings is proper generalization of quasi-normal rings and generalized weakly symmetric rings.We prove that some results of quasi-normal rings and generalized weakly symmetric rings can be extended to WQN rings for this general setting.In particular,it is shown that a ring R is WQN if and only if the n×n upper triangular matrices ring Un(R,R)is WQN for positive integer n.For a WQN ring R,R is strongly regular if and only if R is regular;R is weakly clean if R and only if R is weakly exchange.For applications,we investigate the commutativity of semiperiodic rings when is WQN.
Keywords：weakly quasi-normal ringsquasi-normal ringsgeneralized weakly symmetric ringsweakly clean ringssemiperiodic rings
Publication Date：2024-03-30
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：5( 1-5 )